Panel Data Econometrics This page intentionally left blank Panel Data Econometrics Theory Edited By Mike Tsionas Academic Press is an imprint of Elsevier 125 London Wall, London EC2Y 5AS, United Kingdom 525 B Street, Suite 1650, San Diego, CA 92101, United States 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom © 2019 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. 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This page intentionally left blank Contents Contributors xv Foreword xvii General Introduction xix 1. A Synopsis of Econometrics 1 Stephen G. Hall 1 Introduction 1 2 Some Basic Concepts 2 3 Two Basic Approaches to Estimation 5 4 Maximum Likelihood (ML) 5 5 Generalized Method of Moments (GMM) 10 6 Some Examples of Moment Conditions 12 7 The Standard Linear Model and Least Squares 13 8 Failure of E(uu0) 5 σ2I 14 9 The Vector xt is Stochastic 14 lim ÀÁ0 10 Failure of x u ¼ 014 t ! ∞ T lim ÀÁ0 11 Failure of x x ¼ Ω 15 t ! ∞ T 12 Cointegration 16 13 Conclusion 17 Appendix Order of Magnitude and Convergence 18 References 19 2. Testing and Correcting for Endogeneity in Nonlinear Unobserved Effects Models 21 Wei Lin and Jeffrey M. Wooldridge 1 Introduction 21 2 Models Linear in Parameters 23 3 Exponential Model 28 3.1 An FE Poisson/CF Approach 28 3.2 Estimating Average Partial Effects 30 3.3 A CRE/Control Function Approach 31 4 Probit Response Function 32 5 Other Nonlinear Models 34 vii viii Contents 5.1 Pooled Methods 34 5.2 Joint Estimation Methods 35 6 Empirical Example 36 7 Extensions and Future Directions 38 Appendix 39 A.1 Relationship Between the FE and Mundlak Residuals 39 A.2 Equivalence in Using the FE and Mundlak Residuals in FE Poisson Estimation 40 References 42 Further Reading 43 3. Nonlinear and Related Panel Data Models 45 William Greene and Qiushi Zhang 1 Introduction 45 2 Nonlinear Models 48 2.1 Coefficients and Partial Effects 50 2.2 Interaction Effects 51 2.3 Identification Through Functional Form 51 2.4 Endogeneity 52 3 Panel Data Models 53 3.1 Objects of Estimation 54 3.2 General Frameworks 58 3.3 Dynamic Models 60 4 Nonlinear Panel Data Modeling 61 4.1 Fixed Effects 61 4.2 Random Effects Estimation and Correlated Random Effects 68 4.3 Robust Estimation and Inference 71 4.4 Attrition 73 4.5 Specification Tests 74 5 Panel Data 76 6 Modeling Frameworks and Applications 78 6.1 Binary Choice 78 6.2 Bivariate and Recursive Binary Choice 84 6.3 Ordered Choice 85 6.4 Censored or Truncated Regression 85 6.5 Stochastic Frontier: Panel Models 85 6.6 Count Data 86 6.7 A General Nonlinear Regression 88 6.8 Sample Selection Models 88 6.9 Individual Choice and Stated Choice Experiments 89 6.10 Multilevel Models Hierarchical (Nonlinear) Models 90 6.11 Fixed Effects With Large N and Large T 90 References 91 Contents ix 4. Nonparametric Estimation and Inference for Panel Data Models 97 Christopher F. Parmeter and Jeffrey S. Racine 1 Introduction 97 2 How Unobserved Heterogeneity Complicates Estimation 98 3 Estimation in the Random Effects Framework 99 3.1 Preliminaries 99 3.2 Local-Polynomial Weighted Least-Squares 100 3.3 Spline-Based Estimation 103 3.4 Profile Likelihood Estimation 106 4 Estimation in the Fixed Effects Framework 108 4.1 Differencing/Transformation Methods 108 4.2 Profile Estimation 110 4.3 Marginal Integration 112 4.4 Profile Least Squares 113 5 Dynamic Panel Estimation 116 5.1 The Static Setting 117 6 Inference 118 6.1 Poolability 118 6.2 Specification Testing 122 6.3 A Hausman Test 124 6.4 Simultaneous Confidence Bounds 125 7 Conclusions 127 Acknowledgments 127 References 127 5. Heterogeneity and Endogeneity in Panel Stochastic Frontier Models 131 Levent Kutlu and Kien C. Tran 1 Introduction 131 2 Panel Stochastic Frontier Models With Heterogeneity 132 3 Panel Stochastic Frontier Models With Endogeneity 138 4 Panel Stochastic Frontier Models With Both Heterogeneity and Endogeneity 141 5 Concluding Remarks 143 References 143 6. Bayesian Estimation of Panel Count Data Models: Dynamics, Latent Heterogeneity, Serial Error Correlation, and Nonparametric Structures 147 Stefanos Dimitrakopoulos 1 Introduction 147 2 Bayesian Preliminaries 150 2.1 Bayesian Statistics 150 x Contents 2.2 Markov Chain Monte Carlo Simulation Methods 150 2.3 Bayesian Nonparametric Models 152 3 Parametric Panel Count Data Regression Models 157 3.1 The Static Poisson Model 157 3.2 Extension I: The Dynamic Poisson Model 157 3.3 Extension II: The Dynamic Poisson Model With Latent Heterogeneity 158 3.4 Extension III: The Dynamic Poisson Model With Latent Heterogeneity and Serial Error Correlation 159 4 Semiparametric Panel Count Data Regression Models 160 5 Prior-Posterior Analysis 161 5.1 The Models of Interest 161 5.2 Prior Specification 162 5.3 Posterior Sampling 162 5.4 Model Comparison 170 6 Conclusions 171 References 171 Further Reading 173 7. Fixed Effects Likelihood Approach for Large Panels 175 Chihwa Kao and Fa Wang 1 Introduction 175 2 Notations and Preliminaries 177 3 Fixed Dimensional Case 179 3.1 Consistency 179 3.2 Asymptotic Expansion 180 3.3 Bias Calculation 181 4 Panel With Individual Effects 181 4.1 Consistency 181 4.2 Asymptotic Expansion 182 4.3 Bias Calculation 188 5 Panel With Individual Effects and Time Effects 188 5.1 Consistency 189 5.2 Asymptotic Expansion 189 5.3 Bias Calculation 193 6 Conclusions 195 Acknowledgment 195 References 196 8. Panel Vector Autoregressions With Binary Data 197 Bo E. Honore and Ekaterini Kyriazidou 1 Introduction 197 2 The Univariate Logit Model 199 2.1 Static Case 199 Contents xi 2.2 Dynamic Case (Pure AR(1)) 202 2.3 Dynamic Case With Exogenous Covariates 204 3 The Bivariate Pure VAR(1) Logit Case 206 4 The Bivariate Logit Model With Exogenous Covariates 209 5 The General M-Variate, General T VAR(1) Case 212 6 Contemporaneous Cross-Equation Dependence 213 6.1 Static Case 213 6.2 Dynamic Case 216 7 Monte Carlo Experiments 219 8 Conclusions 220 Acknowledgments 221 References 221 9. Implementing Generalized Panel Data Stochastic Frontier Estimators 225 Subal C. Kumbhakar and Christopher F. Parmeter 1 Introduction 225 2 Earlier Models and Shortcomings 226 3 The Generalized Panel Data Stochastic Frontier Model 230 3.1 Plug-in Estimation 232 3.2 Full Maximum Likelihood 236 3.3 Maximum Simulated Likelihood 239 4 Including Determinants of Inefficiency 240 4.1 Semiparametric Approaches 242 5 Recent Applications of the Generalized Panel Data Stochastic Frontier Model 244 6 Conclusion 246 Acknowledgment 246 References 246 10. Panel Cointegration Techniques and Open Challenges 251 Peter Pedroni 1 Introduction 251 2 Cointegration and the Motivation for Panels 254 3 Strategies for Treating Cross-sectional Heterogeneity in Cointegration Testing and Inference 258 4 Treating Heterogeneity in Residual Based Tests for Cointegration 259 5 Comparison of Residual Based and Error Correction Based Testing 263 6 Estimation and Testing of Cointegrating Relationships in Heterogeneous Panels 266 7 Testing Directions of Long-Run Causality in Heterogeneous Cointegrated Panels 270 xii Contents 8 Strategies for Treating Cross-Sectional Dependence in Heterogeneous Panels 274 9 A Nonparametric Rank Based Approach to Some Open Challenges 277 10 New Directions and Challenges for Nonlinear and Time Varying Long-Run Relationships 282 References 286 11. Alternative Approaches to the Econometrics of Panel Data 289